because she would become the mother of all the living.
God says that now that mankind has the knowledge of good and evil, they must not be allowed to eat from the tree of life, lest they live forever. It is not that God is frightened of what they can accomplish, but he may be limiting their potential for evil. Now that they have to struggle with the sinful nature, it would not be good for them to have an unlimited lifespan as well, lest they become proud and think that they do not need God for anything. Also, perhaps God is using this limitation upon their lifespans to draw people back to Himself. Knowing that they were beings with a limited lifespan might make mankind want to seek God, who holds their lives in His hand, and who can give eternal life.
The LORD banishes Adam and Eve from the Garden of Eden. To guard against anyone trying to sneak back in, cherubim were stationed at the east side of the Garden, armed with a flaming sword which flashed back and forth, guarding the way to the tree of life.